The present invention relates to a new and distinct variety of peach tree named ‘NJ351’. Our new tree resulted from crossing ‘NJ304’ as the seed parent with ‘J19-19-862144’ peach tree, as the pollen parent. The new variety differs from seed parent ‘NJ304’ (unpatented) in that the new variety has firm fruit with yellow flesh while the parent has soft fruit with white flesh. The new variety differs from pollen parent ‘J19-19-862144’ (unpatented) in that the new variety has fruit with a bright ground color and yellow flesh, while the parent has fruit with a slight green ground color and white flesh. The resulting tree was selected when growing in a cultivated area as the 34th tree in the 40th row of Block K in Cream Ridge, N.J.